Crossover effects in a general spin-1-bilinear-biquadratic exchange Hamiltonian

The authors have investigated the general 1D spin-1 bilinear-biquadratic exchange Hamiltonian by analytic and numerical techniques over the range 0<or= beta infinity . The limit beta =0 corresponds to the 1Dd Heisenberg antiferromagnet, the limit beta =1 corresponds to a Bethe ansatz integrable model and beta = infinity corresponds to pure antiferromagnetic biquadratic exchange. Haldane has predicted the existence of a singlet-triplet excitation gap in the thermodynamic limit for beta =0, whereas the beta =1 model is gapless. The authors have studied the singlet-triplet gap by scaled-gap (finite-size scaling) techniques, and it appears to vanish at an intermediate value of beta , with large uncertainty. Finite-system analytic studies show that a fundamental 'two-string' excitation picture describes the spectral excitations in the beta =1 limit, whereas a very different 'single-spin-deviation' picture characterises the excitations in the Heisenberg limit. The crossover between the two pictures shows interesting features and appears to be related to the disappearance of the singlet-triplet gap. The implication of an extended crossover region (1/3< beta <0.62) is discussed in the context of non-integrability effects. Finally, they find the singlet-triplet gap reappears for beta >1.